Bosonization of ZF Algebras: Direction Toward Deformed Virasoro Algebra

TL;DR

This paper reviews bosonization techniques in conformal field theory and applies them to represent ZF algebras, leading to explicit realizations of deformed Virasoro algebra operators with elliptic matrix relations.

Contribution

It provides a novel bosonic construction of chiral vertex operators for the deformed Virasoro algebra using elliptic IRF-type matrices.

Findings

Explicit realization of chiral vertex operators interpolating between irreducible representations.

Operators' commutation relations are governed by elliptic IRF matrices.

Matrix elements expressed as contour integrals of meromorphic functions.

Abstract

These lectures were prepared to be presented at A.A. Belavin seminar on CFT at Landau Institute for Theoretical Physics. We review bosonization of CFT and show how it can be applied to the studying of representations of Zamolodchikov-Faddeev (ZF) algebras. In the bosonic construction we obtain explicit realization of chiral vertex operators interpolating between irreducible representations of the deformed Virasoro algebra. The commutation relations of these operators are determined by the elliptic matrix of IRF type and their matrix elements are given in the form of the contour integrals of some meromorphic functions.